Originally Posted by

**pberardi** Below *f* is a function from a set *A* to a set *B*, and *g* is a function from the set *B* to a set *C*.

**Property 1: If ***f* and *g* are surjections, then *gf*** is a surjection. **

**Proof of Property 1**:

Let *z* an arbitrary element in *C*.

Then since **g** is a surjection, there is an element *y* in *B* such that *z* = **g**(y). Then since **f** is a surjection, there is an element *x* in *A* such that *y* = **f**(x). Hence by the definition of composite function, *z* = **g**(**f**(x)), that is *z* = **gf**(x). Hence **gf** is a surjection. QED

I took this off of a website. I am wondering about its accuracy. Particularly the red line. Shouldn't it be something to the effect:

Since g is a surjection, there is an element y in **B** such that z = g(y)?